Is linking playing to the father's death, and the resulting aversion to playing and fear of practicing it, considered a bad omen?

Your gaming has no connection to your father's death. You must rid yourself of the pathological thoughts causing depression by striving against your lower self (nafs) and remembering that everything is by Allah's permission and mercy. There is no sin upon you for these thoughts that enter your heart, but strive to treat them and live your life normally. If you succumb to them and abandon something permissible for fear of a calamity, that could be from the blameworthy tiyarah (superstitious omens), for "Indeed, tiyarah is only what compels you to proceed or holds you back." And what overwhelms you and you are unable to repel, you are not sinful for it.